Def Sci J, Vol 32, No.

1 , January 1982, pp 47-54

Some Aspects in the Design of Sonar bomes

Received 24 November 1980

Abstract. The importance of vibro-acoustic characteristics in the design of hitherto

conventional Sonar Domes is discussed. A practical method of studying full scaledomes for their vibro-acoustic characteristics is suggested.

1. Introduction

A large number of ships such as research vessels, fishing crafts, warships, etc. are provided With sonars for different applications. All sonars are mounted inside freeflooding domes. In early days, sonar domes for all sonar applications were designedfrom mechanical strength and low drag considerations rather than vibro-acousticcharacteristics. The dome was viewed as an acoustically transparent streamlined bodyto avoid direct interaction of flow with sonar array and at the same time offering goodmechanical strength to overcome the hydrodynamic forces resulting from movementthrough water at maximum speed of the vessel in all weather conditions and ensuingship motions. An attempt is made in this paper to highlight certain aspects to be considered in the design and location of a sonar dome from vibro-acoustic considerationsto reduce sonar self-noise and'thereby improve its detection capability.

2. AnaIysis of the Problem

ZJJany ship's sonar system, the main sources of self-noise operating simultaneouslyare : '(i) Machinery generated noise, (ii) Flow noise, and (iii) Propeller noise.Noise sources such as sea ambient noise, electrical noise, general rattles and bangsof loose equipment etc. are however neglected from the discussion. The main paths/mechanism by which the noise from these sources can reach sonar are : (i) Directmechanical vibration transmitted through the transducer dome mountings, (ii)Direct Bow and/or propellar noise excitation, and (iii) Paths through ship's structureradiated into the adjacent water, and then to the dome. Direct mechanical

48

P K Chakravorty & V Bhujanga Rao

vibration contribution is however not relevant to the discussion because isolation

of this vibration can be achieved by proper design and use of antivibration mountings and must be arranged so as to isolate the whole dome structure in the water ifthey are to be effective.The other paths/mechanism by which the acoustic energy is carried to sonarinside the dome will interact with dome body in two ways; they are :(i) Energy will get transmitted into the dome depending upon the acoustic transparency of the dome wall and/or,(ii) The dome wall will get excited into flexural vibrations causing radiation into theinterior of the dome as self-noise.From the above observations, it can be concluded that dome design, from vibroacoustic point of view, should follow the principles of good wall design which cannotbe easily vibration excited while retaining its acoustic transparency at the sonar operating frequency.3. Vibro-Acoustic Characteristics

Some of the characteristics of the dome to be considered in this paper are :(i) Boundarylayer pressure fluctuations on the dome wall, (ii) Acoustic transparency of the domewall, (iii) Structural damping properties, (iv) Size of the dome, (v) Dome wall configuration, (vi) Response due to acoustic excitation, (vii) Ocean wave effects on thedome, (viii) Radiation effects in the dome interior, and (ix) Location of the dome inthe ship's structure.The conceptual ideas on the above vibro-acousticcharacteristics are briefly discussedbelow :( i ) Boundary Layer Pressure Fluctuations

When a fluid flows past the dome wall, a boundary layer, characterized by turbulent flowconditions, involving fluctuating velocities or pressures is formed at certain speed. Lighthill1, page 13 (1952) published a classic paper giving the theory of sound produced byfree-turbulencz. Curlel, page 14 (1955) extended Lighthill's theory to include theeffect of rigid body adjacent to a region of turbulence. He showed and Phillips',page 15 (1956) confirmed that the intensity of radiation from surface pressurefluctuations on the body is proportibnal to the 6th power of the mean flow Machnumber. This gives an indication that for flows over sonar dome, direct radiationfrom boundary layer pressure fluctuations adjacent to dome cannot be of importance.However, these pressure fluctuations can excite dome-wall vibrations which are to belooked into for the mechanism of flow noise. The boundary layer pressure fluctu'ations,amenable to measurement by flush-mounted hydrophones and often called pseudosaund, is the random function that sets the sonar dome into vibration and consequentacoustic radiation into the interior of the dome. In the absence of a good theorywhich can account for flow-induced vibration of curved walls of arbitrary-shapedbodies, a recent and most applicable theory of flow-induced vibration with fluid loadingis that of Straw-Dermann & Christman? They considered the dome as a plate of

Aspects in the Design of Sonar Domes

49

uniform thickness. The normal deflection W(x, y, t ) of a plate immersed in a fluid

and acted upon by a turbulent pressure fluid P ( x , y , t ) on one side is

(Eh3)-- is the flexural rigidity of the plate, h is the plate thickness, E12 1 - a*and G are Young's Modulus and Poisson's Ratio respectively. The terms P , are theacoustic radiation pressures above and below the plate. They derived an expression inacceleration spectral density form.

where D =

A(W)=P(W)

8.05 x 10-2W6Xw2-

dk.Plate & turbulence parameters

It was calculated by Doughlas A. King3 for various frequencies at free stream speedsfor fibre-reinforced plastic plate10-'u2( f ~>')2-

A ( f ) = P ( f ) 4'9

L gradient =

and P ( f ) for plate with zero pressure

3.16 x 10-5p'38*U5U2

Where

mass density of fluid,

S*

displacement boundary layer thickness,

P( f )

turbulent boundary layer pressure fluctuation.

platic thickness,

free stream velocity.

- frequency, and

Though the above theory is able to explain some of the practical results withinsome limits, no rigorous theory is yet developed to explain flow-induced vibrations ofarbitrary shaped bodies. Hence, there is a necessity to rely more upon practicalexperiments on sonar dome for such information. The type of experiments to becarried out is explained at the end of this paper.

(ii) Acoustic Transparency of the Dome

In the well-designed sonar dome, the acoustic transparency should be maximum in thedirection of sonar signal transmission and reception at sonar operating frequency, whileit should be minimum in the direction of noise entering the dome. While it is somewhat easy to identify direction of signal transmission and reception, it is difficult toattribute a particular direction to noise entering the dome. However, noise enters thedome from all directions, though it is possible to identify a certain area of dome whichacts as a noise window for certain intense noise sources and their direction with respect

P K Chakravorfy & V Bhujanga Rao

50

to sonar and sonar dome. For example, a propeller generally constitutes a majorsource of intense noise at certain speeds insonifying the aft position of the dome. Theparameters which affect the dome transmission coefficient or acoustic transparencyare :'(a) Type of material of the dome-wall, (b) Thickness of the dome-wall, (c) Direction of incidence, (d) Shape or geometry of the dome, and (e) Type of wall structureetc. The type of material by which the dome is made should in the first place beacoustically transparznt at the sonar operating frequency. This being inversely proportional to thickness, a compromise is to be made between thickness required for highacoustic transparency and thickness required for the dome to be mechanically strong toovercome the hydrodynamic forces which are generally encountered at maximum speedof a ship in all weather conditions and resulting ship motions. The acoustic transparency also depends on the direction of incidence and shape or geometry dependingupon its location on the ship structure. While calculating the transmission coefficient,it is necessary to consider dome as a body in close proximity to the ship's structure andits position vis-a-vis the ship's propeller or any other intense source. Type of structuralconfiguration such as stiffened structure, sandwich or pre-stressed structure or fibrereinforced material also effects the transmission coefficient.It has been found from literature4, page 181 that below coincidence frequency, thedominent mechanism of sound transmission through plates and walls, involves longitudinal waves. Flexural waves become dominant in wall transmission for frequenciesabove about fc/2 where fc is the critical frequency of the isolator i.e. dome-wall.In case of longitudinal wave, transmission below coincidence frequency through aplate separating water from water like dome-wall, is

whereat is related to Transmission Loss (TL) =-= 10 log at, p is called load factor definedas the ratio of specific radiation resistance of the fluid to the mass reactance of theplate per unit area. TL so obtained is less than 3 dB for frequency less than fc/4. Fortransmission through air to air separation, the TL is purely governed by mass law andincreases with frequency and structural density upto fc/2 and is given by TL = 20log

pwwhere-

POCO

is surface density,

is angular frequency and

poco is

characteristic impedance of the air. For longitudinal waves to be not transmitted

the most effective way is to provide an air column inside the dome between sonarand the propeller.As far as flexural vibrations are concerned the transmission loss depends on 3 termsas shownTL

"OI O l o g ~ lO1og W20 log ~POCO'XOe

where T ~ =T total loss factor. In this, the first term is due to mass law, the second(negative term) is due to damping and the third is an additional term dependent on

Aspects in the Design of Sonar Domes

51

frequency. Applying these principles to sonar dome problems, isolation can be introduced in the dome between the sonar and the propeller. Several things can be done todecrease transmission between the propeller and the sonar. First thing would be toraise the coincidence frequency of the isolator above the frequency range for whichhigh TL is desired. w , , consider angular frequency, is inversely proportional tothickness and TL in the mass law is directly proportional to thickness. As a compromise, Kurtze & Watter's4, page 184 proposal may be applicable to sonar domes. Thismethod reduces the flexural wave speed without sacrificing mass by using multi-layerplates in which viscous liquid, viscous solid or some material is placed between twoelastic layers.For introducing isolators of this type in sonar domes, extreme care should betaken to isolate the isolator structurally from surrounding vibrating structures, otherwise this baffle will act as an additional radiating surface and give rise to new localsource of noise.(iii) Structural Damping Properties

The effect of increased structural damping on plate vibration and more pertinently onthe resulting radiation is not completely understood. It is Dyer', page 76 (1958) whowas the first to establish some analytical criterion for effectiveness of structuraldamping in reducing flow noise.From his studies, it was established that for frequencies substantially greater thanhydrodynamic critical frequency but less than acoustical critical frequency, a transitionfrequency exists below which a given increase in modal loss factor caused a significantdecrease in modal mean square displacement. Above this frequency, further increaseof E , the loss factor would mzan little effect. The transition frequency as given byDyer is308'ft = 1 where 0 = -

is the temporal decay factor of the turbulent boundary layer; S* = displacement

boundary layer thickness and U = free stream velocity. Dyer calculated for a typifying sonar application where U = 20 ft/sec, '8 = 0.02 ft and 0 = 3 x lo-= sec,ft = 1030 Hz. He found that applied damping treatment should be effective forfrequencies from that of lowest plate mode toft r! 1000 Hz in this case. By this, itwas possible to reduce high Q1s of the order 100 to low Q's of the order 10 by usingapplied damping treatment in case of welded steel structures. Similarly, reduction inthe sound pressure levels of the order of 14-20 dB was realised in tiiese modes.( i v ) Size of the Dome

It has been shown that the external agencieslike flow past the domeexcites bending wavesin the dome-wall structure. Such waves being dispersive in nature, will have velocity ofpropagation along the plate as frequency dependent. Depending on the thickness ofthe plate, below-critical frequency for which the phase velocities along the plate willbe below that of acoustic velocities in water, near-field radiation will take place. Butat critical frequency, phase velocity in the plate and the medium being same, couplingto a wave radiated parallel to the surface of the dome-wall will be experienced. How-

52

P K Chakravorty & V Bhujanga Rao

ever, above critical frequency, the phase velocities in the structure will be greater thanin the phase velocities in the medium and more energy will be radiated at angles otherthan parallel to dome-wall. The far-field radiation effects being very small, the sonararray will be exposed to near-field radiation effects of dome-wall. The size of the domeshould be selected in such a way as to give sufficient clearance of the dome-wall fromthe array to allow the near-field radiation to decay adequately.(v) Dome Wan ConfigurationIn practice dome walls are being fabricated out of plates with periodically spacedbeams or stiffeners or with lot of discontinuities. Any discontinuity or beam attachedto a plate has three distinct effects : (i) it changes its resonance frequency, (ii) when avibrating force excites one region of the plate, it acts to attenuate the vibratory velocities experienced at the other side, (iii) it increases the sound radiated by the plate.Heckel4,page 177 measured transmission through single 2.5 cm high steel beam on a1mm thick aluminium plate in air and found it to vary from 15 to 35 dB. But this valuewill, however, be small in water due to near-field acoustic disturbances. SimilarlyMaidnik, page 178 (1962) Plakov4, page 178 (1967) found that periodically spaced ribsincrease radiation from a plate by 6 dB underwater loading.Now, on the face value, it appears that whether the wall structure for a dome is tobe periodically spaced with ribs depends upon whether vibration propagation along thelength of the wall is to be attenuated at the cost of increase in radiation. However,if propeller noise excitations or turbulent flow fields closer to the aft of the dome-walldominate, it will be worthwhile to go in for rib structure beyond mid aft to attenuatevibration propagation from aft end to forward. The increase in radiation due to suchrib structure (energy absorbers) being concentrated at the aft end of dome, can becounteracted by suitable isolators incorporated in between sonar and the propeller(inside the dome) as discussed earlier. However, it must be remembered that in caseof flow-induced vibration of the dome, such rib structure may be counter-productivedue to additional radiation.(vi) Response Due to Acoustic ExcitationPropeller noise can easily excite dome-wall vibration. Such excitation is dominantonly above coincidence frequencies. The effect of coincidence frequency on dome-wallvibration and self-noise has already been explained in previous paragraphs.(vii) Ocean Wave E'ects on the Dome

Ocean waves cause impact Forces on the sonar domes readily exciting into strongstructural vibration generating high self-noise. Repeated impacts can be found tohave a frequency spectrum flat upto w e (3z)-& and decreases 6 dB per octave forwz > 3 where z is time constant in which the velocity decays to e-I of its initial value.The actual vibration spectrum of the dome structure is, this input spectrum multipliedby the dome-wall response spectrum. Therefore, highest vibratory and acoustic levelscan be expected when harmonics of the impact coincides with structural resonances.Because such coincidences are virtually unavoidable, use of structural damping t oreduce resonant response is especially important in reducing impact noise in dome.

Aspects in the Design of Sonar Domes

53

(viii) Radiation Eflecrs in Dome Interior

So far, the study has been concentrated on dome-wall vibration and their control. Ithas also been said that vibrations being flextural in nature cause acoustic radiationboth outside and inside the dome. The internal radiation is detected at sonar as selfnoise. But in reality, how this radiation effects the self-noise as measured by sonararray depends on such factors as reverberation in the dome, specular, reflection,absorption coefficient of the wall etc. Hence the actual self-noise measured by thearray is the spatial average of the intensity in all the wave lengths over a givenperiod of response. However, how these factors influence the self-noise is yet to bestudied.(ix) Location of Dome in Ship9sStructureThe location of sonar dome also plays a vital part in reducing self-noise. Even if thedome is designed free from turbulent boundary layer on its surface, if the dome is notlocated beyond the immediate boundary layer surrounding the ship's hull, the domewill still be excited by ship's boundary layer pressure fluctuation giving rise to selfnoise. To avoid this, it is necessary to extend out the dome into free-stream water.Another important consideration for location of dome is with respect to propeller ofthe ship. It has been found that whenever a source and a receiver are placed below aplate, the plate acts as a reflector for large angles of incidence, but at grazing incidenceangles, all plates under water loading will transmit the energy through flexural vibrations of the hull. There will be good amount of attenuation in the direct centrinutionintroduced between the source and the receiver for grazing angles and qualitatively theattenuation is found to be of the order of 4th power of the grazing paths. Close toship hull, the propeller and the sonar will act as a pair of such source and receiver, theplate being the ship9shull. The direct path between the propeller and the sonar can,however, be isolated by introducing isolators as discussed earlier. From above considerations, since sonar and dome are inseparable, the self-noise generated will dependupon its location on the ship3sstructure.

4. Practical ApproachAll the phenomena discussed in previous paragraphs is not amenable to any simpletheory because of their varied manifestations. It is proposed that the best method ofanalysing the self-noise problems in sonar domes would be to conduct a series ofpractical experiments and progressively see the effect of each phenomenon on selfnoise.The limitations of such experiments are :(i) The water tunnels are not useful for carrying out such experiments. This ismostly because full scale domes are to be experimentally studied to evaluate certainphenomenon like reverberation effects,near field effects, effect of sonar transducer whichoccupy a significant volume, shadowing effects, stiffening effects, direction of radiationetc. due to their complexity in formulating scaling laws.(ii) The ambient noise is generally quite high either in towing basins or watertunnels which precludes their use.

54

P K Chakravorty & V Bhujanga Rao

(iii) The acoustic wave lengths generally encountered in these experiments are sogreat that the water tunnels are not of much service because of very close boundaries.After careful study of all the possibilities, it has been realised by the authors thatthe best way of studying self-noise in domes would be by use of buoyant or gravitypropelled sonar domes. For this purpose an actual-size dome is made. to either popoff under buoyancy or go-down under gravity in a lake of considerable depth andsize. Different terminal speeds can b: achieved for different loadings. Theequation of motion, for gravity propeller dome is

and for buoyancy propelled dome is

velocity of vehicle, A = surface area, m = mass of the body. If the initial accelerationis zero, RHS will be zero, the motion of the body will be uniform and attain terminalvelocity V which can be easily calculated.For such experiments, sometimes, domes of certain shapes may require slightmodification like making them somewhat axisymmetric to ensure uniform flow allaround the body. The dome is then to be fitted with sufficient number of flushmounted pressure transducers for pressure measurement; accelerometers for recordingwall vibration and one or two hydrophones in place of sonar array for finding out selfnoise for different types of studies such as flow induced vibration etc. If necessary,these experiments can be extended to generate turbulence by artificial means of trippingand observe its effect on self-noise. Similarly, studies on self-noise due to reverberation effects, near-field noise; cavitation-excited noise etc. can be carried out on suchmodels.